x^2/x+5+10=25/x+5

Solution for x^2/x+5+10=25/x+5 equation:

x^2/x+5+10=25/x+5

We move all terms to the left:

x^2/x+5+10-(25/x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+5)!=0

x∈R


We add all the numbers together, and all the variables

x^2/x-(25/x+5)+15=0

We get rid of parentheses

x^2/x-25/x-5+15=0

We multiply all the terms by the denominator


x^2-5*x+15*x-25=0

We add all the numbers together, and all the variables

x^2+10x-25=0

a = 1; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·1·(-25)
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{2}}{2*1}=\frac{-10-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{2}}{2*1}=\frac{-10+10\sqrt{2}}{2}
$